Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session Y28: Rods & Buckling |
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Sponsoring Units: GSNP Chair: Basile Audoly, University Paris 6 Room: 336 |
Friday, March 22, 2013 8:00AM - 8:12AM |
Y28.00001: Three-dimensional Curling of Pre-strained Elastomeric Strips: From Hemi-helix to Helix Jia Liu, Jiangshui Huang, Tianxiang Su, Katia Bertoldi, David Clarke A variety of three dimensional curls can be produced by a simple generic process consisting of pre-straining one elastomeric strip, joining it to another and then releasing the bi-strip. In thin strips we observe the formation of hemi-helices, which consists of multiple, alternating helical sections of half wavelength in opposite chiralities, separated by perversions. By contrast, helical shapes with uniform handedness are found when the cross-section is wide and flat. Finally, in the transition region between helices and hemi-helices not only the geometry effects but also boundary conditions as well as dynamic effects severely contributes. The phase separation of hemi-helical and helical structures has similarities with coiled polymer molecules and plant tendrils. [Preview Abstract] |
Friday, March 22, 2013 8:12AM - 8:24AM |
Y28.00002: A rod theory for pleated elastic strips Basile Audoly, Marcelo Dias We consider the equilibrium shapes of a thin, annular strip cut out in a sheet of paper: when such a strip is folded along its circular centerline, it has been observed to buckle out-of-plane (Dias et al., PRL, 2012). We derive an equivalent Kirchhoff rod model for the folded strip. A nonlinear effective constitutive law capturing the underlying geometrical constraints is derived. In this rod model, the opening mode of the ridge appears as an internal degree of freedom. The buckling of the strip is shown to be equivalent to the buckling of a circular ring having two frozen curvatures. Another type of instability is pointed out, whereby the centerline remains planar but the ridge angle is modulated. [Preview Abstract] |
Friday, March 22, 2013 8:24AM - 8:36AM |
Y28.00003: Buckling of a Flexible Strip Sliding on a Frictional Base Alexandre Huynen, Julien Marck, Vincent Denoel, Emmanuel Detournay The main motivation for this contribution is the buckling of a drillstring sliding on the bottom of the horizontal section of borehole. The open questions that remain today are related to the determination of the onset of instability, and to the conditions under which different modes of constrained buckling occur. In this presentation, we are concerned by a two-dimensional version of this problem; namely, the sliding of a flexible strip being fed inside a conduit. The ribbon, which has a flexural rigidity $EI$ and a weight per unit length $w$, is treated as an inextensible elastica of negligible thickness. The contact between the ribbon and the wall of the conduit is characterized by a friction coefficient $\mu$. First, we report the result of a stability analysis that aims at determining the critical inserted length of the ribbon $\ell_{*}(\mu)$ (scaled by the characteristic length $\lambda=(EI/w)^{1/3}$) at which there is separation between the strip and the conduit bottom, as well as the buckling mode. Next, the relationship between the feeding force $F$ and the inserted length $\ell$ after bifurcation is computed. Finally, the results of a ``kitchen table'' experiment involving a strip of silicon rubber being pushed on a plank are reported and compared with predictions. [Preview Abstract] |
Friday, March 22, 2013 8:36AM - 8:48AM |
Y28.00004: Better Contact Through Twist? The skew-dependence of inter-filament adhesion Luis Cajamarca, Gregory Grason Adhesive interactions between flexible filaments maximizes their contact, though the geometry of optimal contact is far from obvious. We address a simple question: how does inter-filament twist vary the adhesive energy? We investigate two models for adhesive interactions for filaments: a Lennard-Jones potential (LJP), and a model consisting of opposite interactions, screened electrostatic repulsion and depletion attraction (SED). In both potentials the interaction energy decreases for large twist. However, for small twist the SED potential is metastable whereas the LJP is not. We understand this effect by looking at how distances between patches of area on the surface change with twist. Patches further away come into closer contact as twist increases, effectively increasing the repulsion energy. This in turn pushes the filaments away and the net result is to favor a locally parallel orientation. Finally, we predict how the geometric minima of the interaction energy varies with inter-filament spacing for the LJP, where we observe two regions dominated by geometry: threads regime, where the filaments are very thin and interactions are long-range, and contact regime, where the filaments are very thick tubes and interactions become short-range compared to tube diameter. [Preview Abstract] |
Friday, March 22, 2013 8:48AM - 9:00AM |
Y28.00005: Buckling of an elastic wire inside an elastic matrix Tianxiang Su, Jia Liu, Denis Terwagne, Katia Bertoldi, Pedro Reis Using both experiment and dynamic simulation results, we will discuss in this talk how a compressed elastic wire embedded within an elastic matrix buckles into two dimensional (2D) planar shape and then three dimensional (3D) helical shape. We will show that the transitions from the initial 1D to 2D and then 3D configurations can be tuned by and are highly sensitively to the supporting matrix stiffness. This property may be useful for future photonic and piezoelectric devices. Analytic buckling and post-buckling analysis will also be presented to rationalize our results. [Preview Abstract] |
Friday, March 22, 2013 9:00AM - 9:12AM |
Y28.00006: Buckling of a thin rod under cylindrical constraint Jay Miller, Tianxiang Su, Nathan Wicks, Jahir Pabon, Katia Bertoldi, Pedro Reis We investigate the buckling and post-buckling behavior of a thin elastic rod, under cylindrical constraint, with distributed loading. Our precision model experiments consist of injecting a custom-fabricated rod into a transparent glass pipe. Under imposed velocity (leading to frictional axial loading), a portion of the initially straight rod first buckles into a sinusoidal mode and eventually undergoes a secondary instability into a helical configuration. The buckling and post-buckling behavior is found to be highly dependent on the system's geometry, namely the injected rod length and the aspect ratio of the rod to pipe diameter, as well as material parameters. We quantify the critical loads for this sequence of instabilities, contrast our results with numerical experiments and rationalize the observed behavior through scaling arguments. [Preview Abstract] |
Friday, March 22, 2013 9:12AM - 9:24AM |
Y28.00007: Statistical properties of an elastic rod dynamically confined in 2D Frederic Lechenault, Mokhtar Adda-Bedia We investigate the statistical properties and stationary states of an elastic rod dynamically confined in a Hele-Shaw cell. As the confined length is increased, we observe a transition from an ordered spiral-like pattern to a disordered, rearranging pack of loops. ~In the disordered phase, we decipher the trajectories of the rod from its geometric configurations, and report correlation between curvilinear and spatial energy distributions. Moreover, we establish the relationship between the number of loops and the confined length, yielding insights into the loop occupation number and the overall rigidity of the system. [Preview Abstract] |
Friday, March 22, 2013 9:24AM - 9:36AM |
Y28.00008: Loops, Wrinkles and Scrolls in Twisted Ribbons Julien Chopin, Arshad Kudrolli We explore experimentally the stable and metastable configurations of an elastic ribbon under mixed twist and tension. A ribbon is a slender and thin elastic material with an extremely narrow cross section which exhibits features of rods and plates: it can coil and form loops but wrinkles and stress localization can also been seen yielding a surprisingly rich variety of shapes. Using the twist angle and the tension as control parameters, the various configurations obtained can be rationalized in a phase diagram. Using x-ray tomography, we are able to reconstruct the 3D shape of the ribbon which can then be precisely characterized by measuring locally the mean and Gaussian curvature. Guided by our experimental data, we will present a simple model for the bifurcations observed. Finally, implications for the fabrication of structured rods and yarns with novel mechanical and transport properties will be discussed. [Preview Abstract] |
Friday, March 22, 2013 9:36AM - 9:48AM |
Y28.00009: Explicit solutions for the buckling of an imperfect strut on a nonlinear foundation Romain Lagrange, Daniel Averbuch We perform a theoretical and numerical study of the buckling of an imperfect finite strut on a nonlinear elastic Winkler type foundation. The imperfection is introduced by considering an initially deformed shape which is a sine function with an half wavelength. The length of the strut is chosen such that the first buckling mode is excited and the restoring force is either a bi-linear or an exponential profile. Considering these two profiles, we show (exact piecewise solution theory, explicit Galerkin method, numerical resolution) that the system is subcritical, imperfection sensitive and the deflection is an amplification of the default. For small imperfection sizes, the equilibrium paths hit a limit point which is asymptotic to the Euler load for a critical imperfection amplitude. This critical amplitude is determined analytically and does not depend on the choice of the restoring force. The decrease of the maximum value of the axial force supported by the beam as a function of the imperfection magnitude is determined. We show that the leading term of the development has a different exponent than in subcritical buckling of elastic systems, and that the exponent values depend on the regularization. [Preview Abstract] |
Friday, March 22, 2013 9:48AM - 10:00AM |
Y28.00010: On the tensorial nature of chirality Efi Efrati, William Irvine Chirality occupies a central role in fields ranging from biological self assembly to the design of optical meta-materials. The definition of chirality, as given by lord Kelvin in 1893, associates handedness with the lack of mirror symmetry. However, the quantification of chirality based on this definition has proven to be an elusive task. The difficulty in quantifying chirality is contrasted by the ease with which one determines the handedness of objects with a well defined axis such as screws and helices. In this talk I will present table-top demonstrations that show that a single object can simultaneously be left handed and right handed when considered from different directions. The orientation dependence of handedness motivates a tensorial quantification of chirality relating directions to rotations. I will give an explicit example of such a tensorial measure of chirality for embedded surfaces, and show how the tensorial nature of chirality can be probed in experiments and exploited as a design principle. [Preview Abstract] |
Friday, March 22, 2013 10:00AM - 10:12AM |
Y28.00011: Mechanics and Dynamics of Snapping Beams Anupam Pandey, Derek Moulton, Dominic Vella, Douglas Holmes Snap-buckling is an elastic instability that causes a rapid transition between two states separated by a finite distance. These rapid instabilities occur naturally in plants like the Bunchberry dogwood and the Venus flytrap, yet the dynamics of this phenomenon remain poorly understood. In this talk we discuss the statics and dynamics of the point load snap through of an arch. During deformation, the arch transitions from a symmetric to an asymmetric mode at a critical load and then snap-buckles at a critical indentation height. We will demonstrate that this critical force and displacement for stability loss varies nonlinearly with the amount of initial compression applied to the flat beam, and the dynamics of the snapping arch have an instability growth-rate dictated by the speed of sound within the material. [Preview Abstract] |
Friday, March 22, 2013 10:12AM - 10:24AM |
Y28.00012: Effect of aspect ratio on the stress response of frictional elastic rod assemblies Vikrant Yadav, Arshad Kudrolli We discuss the effect of aspect ratio on the response of a random assembly of frictional elastic rods under repeated top loading stress-strain cycles. Random assemblies of rods of different aspect ratios were created by rain deposition of particles. Considerable hysteresis is observed over the first few cycles, but the response starts to approach a more reversible path with each cycle. The assembly was scanned after each cycle using a 3D X-ray computer aided tomography instrument to determine position, orientation, and contacts of each constituent particle. We show that rods of small aspect ratio pack tend to have small compression under the same stress as compared to rods of higher aspect ratio because they pack more densely, and thus have larger Young's modulus. By tracking motion of constituent rods over subsequent cycles we observed that larger number of rearrangements take place in the bulk away from boundaries. The mean distance over which a particle moves to rearrange also decreases with each cycle. The mean numbers of contacts were also evaluated and were found to increase rapidly with small changes in volume fraction. [Preview Abstract] |
Friday, March 22, 2013 10:24AM - 10:36AM |
Y28.00013: Thin film buckling : a relation between adhesion and morphology Etienne Barthel, Jean-Yvon Faou, Sergey Grachev, Guillaume Parry When thin films with low adhesion are compressively stressed, they may buckle. These buckles exhibit interesting morphologies such as the well known telephone cord. However our understanding of this form of buckling is limited because it couples the large displacement nonlinearities of plates with the subtleties of mixed-mode adhesion. Here we investigate the morphology of the thin film buckles as a function of mode mixity by a combination of experiments and simulations. We first exhibit a linear relation between the period of the telephone cord buckles and a characteristic parameter of the mixed mode adhesion. Furthermore we evidence a rich set of new buckle morphologies through experiments, and demonstrate that these morphologies can be reproduced in the simulations. We also show that we can rationalize the transitions between morphologies through a phase diagram. This excellent agreement between experimental results and numerical predictions further validates the simulation method we have developped recently. [Preview Abstract] |
Friday, March 22, 2013 10:36AM - 10:48AM |
Y28.00014: Use of magnetic micro-cantilevers to study the dynamics of 3D engineered smooth muscle constructs Alan Liu, Ruogang Zhao, Craig Copeland, Christopher Chen, Daniel Reich The normal and pathological response of arterial tissue to mechanical stimulus sheds important light on such conditions as atherosclerosis and hypertension. While most previous methods of determining the biomechanical properties of arteries have relied on excised tissue, we have devised a system that enables the growth and in situ application of forces to arrays of stable suspended microtissues consisting of arterial smooth muscle cells (SMCs). Briefly, this magnetic microtissue tester system consists of arrays of pairs of elastomeric magnetically actuated micro-cantilevers between which SMC-infused 3D collagen gels self-assemble and remodel into aligned microtissue constructs. These devices allow us to simultaneously apply force and track stress-strain relationships of multiple microtissues per substrate. We have studied the dilatory capacity and subsequent response of the tissues and find that the resulting stress-strain curves show viscoelastic behavior as well as a linear dynamic recovery. These results provide a foundation for elucidating the mechanical behavior of this novel model system as well as further experiments that simulate pathological conditions. [Preview Abstract] |
Friday, March 22, 2013 10:48AM - 11:00AM |
Y28.00015: Pattern formation by deposition of a thin elastic rod on a moving substrate Mohammad Khalid Jawed, Fang Da, Eitan Grinspun, Pedro Reis We report on the formation of coiling patterns when a thin elastic rod is deposited onto a moving solid boundary. We combine precision model experiments with cutting-edge computational mechanics tools ported from the computer graphics community. In our experiments, we deposit elastomeric rods onto a conveyor belt. Our numerical tool simulates the experimental scenario by implementing a discrete notion of bending and twist of the thin rod, based on discrete differential geometry, exhibiting excellent performance and robustness. The synergy between experiments and numerics, and the excellent agreement between the two, allows us to identify the key physical ingredients of the process, explore the phase diagram of the system, quantify the influence of the control parameters and rationalize the underlying mechanical instabilities. The gained predictive understanding of this geometrically-nonlinear pattern formation process has potential applications ranging from the micron-scale (coiling of carbon nanotubes) to the kilometer-scale (laying down of transoceanic undersea cables). [Preview Abstract] |
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